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Register a new user$Omega$-Slow Solutions and Be Star Disks
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As the disk formation mechanism(s) in Be stars is(are) as yet unknown, we investigate the role of rapidly rotating radiation-driven winds in this process. We implemented the effects of high stellar rotation on m-CAK models accounting for: the shape of the star, the oblate finite disk correction factor, and gravity darkening. For a fast rotating star, we obtain a two-component wind model, i.e., a fast, thin wind in the polar latitudes and an $Omega$-slow, dense wind in the equatorial regions. We use the equatorial mass densities to explore H$alpha$ emission profiles for the following scenarios: 1) a spherically symmetric star, 2) an oblate shaped star with constant temperature, and 3) an oblate star with gravity darkening. One result of this work is that we have developed a novel method for solving the gravity darkened, oblated m-CAK equation of motion. Furthermore, from our modeling we find a) the oblate finite disk correction factor, for the scenario considering the gravity darkening, can vary by at least a factor of two between the equatorial and polar directions, influencing the velocity profile and mass-loss rate accordingly, b) the H$alpha$ profiles predicted by our model are in agreement with those predicted by a standard power-law model for following values of the line-force parameters: $1.5 lesssim k lesssim 3$, $ , alpha sim 0.6$ and $, delta gtrsim 0.1$, and c) the contribution of the fast wind component to the H$alpha$ emission line profile is negligible; therefore, the line profiles arise mainly from the equatorial disks of Be stars.
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The standard, or fast, solutions of m-CAK line-driven wind theory cannot account for slowly outflowing disks like the ones that surround Be stars. It has been previously shown that there exists another family of solutions --- the $Omega$-slow solutions --- that is characterized by much slower terminal velocities and higher mass-loss rates. We have solved the one-dimensional m-CAK hydrodynamical equation of rotating radiation-driven winds for this latter solution, starting from standard values of the line force parameters ($alpha$, $k$, and $delta$), and then systematically varying the values of $alpha$ and $k$. Terminal velocities and mass-loss rates that are in good agreement with those found in Be stars are obtained from the solutions with lower $alpha$ and higher $k$ values. Furthermore, the equatorial densities of such solutions are comparable to those that are typically assumed in ad hoc models. For very high values of $k$, we find that the wind solutions exhibit a new kind of behavior.
We present an analysis of the near-infrared continuum emission from the circumstellar gas disks of Be stars using a radiative transfer code for a parametrized version of the viscous decretion disk model. This isothermal gas model creates predicted images that we use to estimate the HWHM emission radius along the major axis of the projected disk and the spatially integrated flux excess at wavelengths of 1.7, 2.1, 4.8, 9, and 18 ?m. We discuss in detail the effect of the disk base density, inclination angle, stellar effective temperature, and other physical parameters on the derived disk sizes and color excesses. We calculate color excess estimates relative to the stellar V -band flux for a sample of 130 Be stars using photometry from 2MASS and the AKARI infrared camera all-sky survey. The color excess relations from our models make a good match of the observed color excesses of Be stars. We also present our results on the projected size of the disk as a function of wavelength for the classical Be star ? Tauri, and we show that the model predictions are consistent with interferometric observations in the H, K, and 12 mu m bands.
Evolutionary models of fast-rotating stars show that the stellar rotational velocity may approach the critical speed. Critically rotating stars cannot spin up more, therefore they lose their excess angular momentum through an equatorial outflowing disk. The radial extension of such disks is unknown, partly because we lack information about the radial variations of the viscosity. We study the magnetorotational instability, which is considered to be the origin of anomalous viscosity in outflowing disks. We used analytic calculations to study the stability of outflowing disks submerged in the magnetic field. The magnetorotational instability develops close to the star if the plasma parameter is large enough. At large radii the instability disappears in the region where the disk orbital velocity is roughly equal to the sound speed. The magnetorotational instability is a plausible source of anomalous viscosity in outflowing disks. This is also true in the region where the disk radial velocity approaches the sound speed. The disk sonic radius can therefore be roughly considered as an effective outer disk radius, although disk material may escape from the star to the insterstellar medium. The radial profile of the angular momentum-loss rate already flattens there, consequently, the disk mass-loss rate can be calculated with the sonic radius as the effective disk outer radius. We discuss a possible observation determination of the outer disk radius by using Be and Be/X-ray binaries.
The observed emission lines of Be stars originate from a circumstellar Keplerian disk that are generally well explained by the Viscous Decretion Disk model. In an earlier work we performed the modeling of the full light curve of the bright Be star $omega$ CMa (Ghoreyshi et al. 2018) with the 1-D time-dependent hydrodynamics code SINGLEBE and the Monte Carlo radiative-transfer code HDUST. We used the V -band light curve that probes the inner disk through four disk formation and dissipation cycles. This new study compares predictions of the same set of model parameters with time-resolved photometry from the near UV through the mid-infrared, comprehensive series of optical spectra, and optical broad-band polarimetry, that overall represent a larger volume of the disk. Qualitatively, the models reproduce the trends in the observed data due to the growth and decay of the disk. However, quantitative differences exist, e.g., an overprediction of the flux increasing with wavelength, too slow decreases in Balmer emission-line strength that are too slow during disk dissipation, and the discrepancy between the range of polarimetric data and the model. We find that a larger value of the viscosity parameter alone, or a truncated disk by a companion star, reduces these discrepancies by increasing the dissipation rate in the outer regions of the disk.
$gamma$ Cas stars are a $sim$1% minority among classical Be stars with hard but only moderately strong continuous thermal X-ray flux and mostly very early-B spectral type. The X-ray flux has been suggested to originate from matter accelerated via magnetic disk-star interaction, by a rapidly rotating neutron star (NS) companion via the propeller effect, or by accretion onto a white dwarf (WD) companion. In view of the growing number of identified $gamma$ Cas stars and the only imperfect matches between these suggestions and the observations, alternative models should be pursued. Two of the three best-observed $gamma$ Cas stars, $gamma$ Cas itself and $pi$ Aqr, have a low-mass companion with low optical flux; interferometry of BZ Cru is inconclusive. Binary-evolution models are examined for their ability to produce such systems. The OB+He-star stage of post-mass transfer binaries, which is otherwise observationally unaccounted, can potentially reproduce many observed properties of $gamma$ Cas stars. The interaction of the fast wind of helium stars with the disk and/or with the wind of Be stars may give rise to the production of hard X-rays. While not modelling this process, it is shown that the energy budget is favourable, and that the wind velocities may lead to hard X-rays as observed in $gamma$ Cas stars. Furthermore, their observed number appears to be consistent with the evolutionary models. Within the Be+He-star binary model, the Be stars in $gamma$ Cas stars are conventional classical Be stars. They are encompassed by O-star+Wolf-Rayet systems towards higher mass, where no stable Be decretion disks exist, and by Be+sdO systems at lower mass where the sdO winds may be too weak to cause the $gamma$ Cas phenomenon. In decreasing order of the helium-star mass, the descendants could be Be+black-hole, Be+NS or Be+WD binaries.
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